In the case of push-to-talk over cellular, as is specified in the Open Mobile Alliance, participant communication terminals and their users may be simultaneously involved in a plurality of sessions. Since only one data stream can ever be output on the respective participant communication terminal at one time, provision is currently made for a user of a participant communication terminal who has been invited to a communication session to be able to determine during a communication session whether it is intended to be a high-priority communication session (“primary session”) or a lower-priority communication session (“secondary session”) for him.